The spectrum of instantaneous normal mode (INM) frequencies of finite
Lennard-Jones clusters is studied as a function of the extent of quant
um delocalization. Configurations are sampled from the equilibrium dis
tribution by a Fourier path integral Monte Carlo procedure. The INM sp
ectra, average force constants and Einstein frequencies are shown to b
e interesting dynamical markers for the quantum delocalization-induced
cluster solid-liquid transition. Comparisons are made with INM spectr
a of quantum and classical Lennard-Jones liquids. The methodology used
here suggests a general strategy to obtain quantal analogs of various
classical dynamical quantities. (C) 1997 American Institute of Physic
s.